MCQ
$\frac{\cos38^\circ\text{cosec}52^\circ}{\tan18^\circ\tan35^\circ\tan60^\circ\tan72^\circ\tan55^\circ}=?$
- A$\sqrt3$
- B$\frac{1}{3}$
- ✓$\frac{1}{\sqrt3}$
- D$\frac{2}{\sqrt3}$
✓
Answer
Correct option: C.
$\frac{1}{\sqrt3}$
$\frac{\cos38^\circ\text{cosec}52^\circ}{\tan18^\circ\tan35^\circ\tan60^\circ\tan72^\circ\tan55^\circ}$
$=\frac{\cos(90^\circ-52^\circ)\text{cosec}52^\circ}{\tan18^\circ\times\tan35^\circ\times\sqrt3\times\tan(90^\circ-18^\circ)\times\tan(90^\circ-35^\circ)}$
$=\frac{\sin52^\circ\text{cosec}52^\circ}{\tan18^\circ\times\tan35^\circ\times\sqrt3\times\sec18^\circ\times\sec35^\circ}$
$=\frac{\sin52^\circ\times\frac{1}{\sin52^\circ}}{(\tan18^\circ\sec18^\circ)\times\sqrt3\times(\tan35^\circ\sec35^\circ)}$
$=\frac{1}{1\times\sqrt3\times1}$
$=\frac{1}{\sqrt3}$
$=\frac{\cos(90^\circ-52^\circ)\text{cosec}52^\circ}{\tan18^\circ\times\tan35^\circ\times\sqrt3\times\tan(90^\circ-18^\circ)\times\tan(90^\circ-35^\circ)}$
$=\frac{\sin52^\circ\text{cosec}52^\circ}{\tan18^\circ\times\tan35^\circ\times\sqrt3\times\sec18^\circ\times\sec35^\circ}$
$=\frac{\sin52^\circ\times\frac{1}{\sin52^\circ}}{(\tan18^\circ\sec18^\circ)\times\sqrt3\times(\tan35^\circ\sec35^\circ)}$
$=\frac{1}{1\times\sqrt3\times1}$
$=\frac{1}{\sqrt3}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The decimal expansion of the rational number $\frac{33}{15}$ will terminate after.
→If $p$ and $q$ are positive integers such that $p=a b^2$ and $q=a^3 b$, where $a, b$ are prime numbers, then $\operatorname{HCF}(p, q)=$
→A quadratic equation whose roots are $2+\sqrt{3}$ and $2-\sqrt{3}$ is
→If in two triangles $\text{DEF}$ and $\text{PQR}, \angle D=\angle Q$ and $\angle R=\angle E,$ then which of the following is not true?
→If the difference between the circumference and the radius of a circle is $37 \ cm,$ then using $\pi = \frac{22}{7},$ the circumference $($in $\ cm)$ of the circle is :
→In a $\triangle\text{ABC}$ it is given that $AB = 6\ cm, AC = 8\ cm$ and $AD$ is the bisector of $\angle\text{A}.$ Then $, BD : DC =?$
→The sum of the first $20$ terms of the $A.P.\{ 10, 6, 2, ...\}$ is :
→If $\alpha,\beta$ are the zeros of polynomial $f(x) = x^2 - p (x + 1) - c$, then $(\alpha+1)(\beta+1)=$
→The circumference of a circle is 100 cm . The side of a square inscribed in the circle is
Decimal expansion of $\frac{23}{\left(2^3 5^2\right)}$ will be:
→